Forming a hypothesis for a research paper

This trend is fully confirmed in the check-list choices. In Table 2 we report the frequency (in terms of percentages) with which each term in the check list was selected. For the sake of brevity of presentation we state the results for the positive term in each pair; the reader may determine the percentage of choices for the other term in each pair by subtracting the given figure from 100. To illustrate, under Condition A of the present experiment, 91 per cent of the subjects chose the designation "generous"; the remaining 9 per cent selected the designation "ungenerous." Occasionally, a subject would not state a choice for a particular pair. Therefore, the number of cases on which the figures are based is not always identical; however, the fluctuations were minor, with the exception of the category "good-looking— unattractive," which a larger proportion of subjects failed to answer.

The PIH helps explain the failure of transitory Keynesian demand management techniques to achieve its policy targets. [2] In a simple Keynesian framework the marginal propensity to consume (MPC) is assumed constant, and so temporary tax cuts can have a large stimulating effect on demand. The PIH framework suggests that a consumer will spread out the gains from a temporary tax cut over a long horizon, and so the stimulus effect will be much smaller. There is evidence supporting such a view, . Shapiro and Slemrod (2003). [12]

Besides considering experimental results, numerical models are frequently used to examine the mechanical response of polycrystalline materials. Micromechanical models based on CP theory play a significant role in understanding yielding and anisotropy of metals, as well as in evaluating yield surface models. The earliest of such approaches, proposed by Sachs (1929),
uses an iso-stress approach and assumes the same resolved stress on the slip systems with the highest resolved shear stress in all grains within the polycrystalline aggregate. In contrast, the full-constraint (FC) model developed by Taylor (1938) is based on the iso-strain assumption, ., all grains within an aggregate experience the same state of deformation. The FC TAYLOR model
was elaborated further by Bishop and Hill (1951), and was used as the TAYLOR-BISHOP-HILL (TBH) model by many researchers to validate yield functions (Hosford, 1972; Barlat and Lian, 1989; Barlat et al., 1997) or to generate the analytical expressions for plastic potentials and yield surfaces of anisotropic polycrystalline materials (Gambin, 1991; Van Houtte, 1994, 2001; Li et al.,
2003; Van Houtte and Van Bael, 2004; Kowalczyk and Gambin, 2004; Van Houtte et al., 2009). It should be noted that the SACHS model satisfies the stress equilibrium condition across the grains but violates the compatibility condition between them, while, in contrast, the TBH model violates the stress equilibrium condition but satisfies the compatibility condition among differently oriented grains (Kocks, 1958). The deformation behavior of real polycrystals, where both, compatibility and equilibrium are fulfilled, is in-between these two extremes (Sachtleber et al., 2002). The former model therefore sets the lower bound and the latter is the upper bound of the observed behavior.
Although the TAYLOR model shows good performance in the prediction of deformation textures, it is not fully realistic due to the violation of stress equilibrium. Various relaxed-constraint (RC) TAYLOR models were developed relieving the rigid deformation constraint in TAYLOR's iso-strain hypothesis (Honneff and Mecking, 1981; Kocks and Chandra, 1982; Raphanel and Van
Houtte, 1985; H€olscher et al., 1991, 1994; Raabe, 1995c). Also, a number of grain cluster models were introduced such as the LAMEL model, the advanced LAMEL (ALAMEL) model (Van Houtte et al., 1999, 2002, 2005), the grain interaction (GIA) model (Raabe,1995a,b; Raabe et al., 2002b; Crumbach et al., 2006), and the relaxed grain cluster (RGC) model (Tjahjanto et al., 2010).
Another important class of homogenization schemes is based on the self consistent (SC) approach which was originally proposed by Kr€oner (1958) for the elastic case and later extended to the elastoplastic (Hill,1965) and viscoplastic (Hutchinson, 1976) cases. In the SC theory, each grain within a polycrystalline aggregate is considered to be an ellipsoidal inclusion
embedded in the surrounding homogeneous equivalent medium (HEM). Such models satisfy the stress equilibrium and the deformation compatibility simultaneously as they allow for different deformation responses in each grain depending on the relative stiffness between the grain and the HEM. Among the various SC models, the visco-plastic self consistent (VPSC) model
developed by Molinari et al. (1987) and extended by Lebensohn and Tom!e (1993, 1994) has been widely used to simulate plastic behavior and texture evolution of polycrystalline materials (Lebensohn et al., 1996, 1998; Segurado et al., 2012; Knezevic et al., 2013). Although the SC models relieve the drawbacks associated with the TAYLOR type models, further microstructural aspects of the deformation, such as local grain interaction and intra-grain inhomogeneities of the micromechanical fields, are not accessible to these models (Zhao et al., 2007; Lebensohn et al., 2012).

Forming a hypothesis for a research paper

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